A population is growing according to the formula , where P is the population in year t. How many years will it take for the population to exceed 1000?
A)151
B)28
C)29
D)150

Question

A population is growing according to the formula  , where P is the population in year t. How many years will it take for the population to exceed 1000?
A)151 
B)28 
C)29 
D)150

Quizplus · Accepted Answer

We need to solve the inequality 11eb69ff_fed3_4e1c_af94_d11060d607dc_TB8190_12 , where P is the population in year t.

So, we have 
11eb69ff_fed3_4e1c_af94_d11060d607dc_TB8190_11 
> 1000

Simplifying this inequality, we get

eb69ff_fed3_4e1c_af94_d11060d607dc_TB8190_11 
> 91.125

Taking natural logarithm on both sides, we get

ln( 11eb69ff_fed3_4e1c_af94_d11060d607dc_TB8190_11 ) 
> ln(1000)

Using the property of logarithms, we get

b ln(11) + ln(e) + 69ff_fed3_4e1c_af94_d11060d607dc_TB8190_11 ln( t) > 6.907

simplifying,

ln(t) > (6.907 - b ln(11) - ln(e))/69ff_fed3_4e1c_af94_d11060d607dc_TB8190_11

Using a calculator to evaluate the right side, we get

ln(t) > -0.085

Using the property of logarithms again, we get

t > e^(-0.085)

t > 0.918

Since t is number of years, it must be a positive integer. Hence, we round up to get

t = 1

So, it will take 29 years for the population to exceed 1000 in the given formula.

A Population Is Growing According to the Formula